Interfacial area per molecule

FIG. 29 Oxygen-transfer rate constants derived from Fig. 28 as a function of the reciprocal of the interfacial area per molecule. (Reprinted from Ref 19. Copyright 1998 American Chemical Society.)... 

Bq is the interfacial area per molecule (depends on the size and hydration of the polar head)... 

Table 8.4 Calculated d spacings from measured and indexed Bragg peaks for hexagonal and cubic Si CjEOsi 6/D4 mixtures at 58°C, and derived micellar core radius Reore and interfacial area per molecule, as.

In fact, the predominant forces determining association of amphiphiles in well defined structures (e.g., micellar, cylindrical, lamellar) are the hydrophobic effect, tending to associate chains together, and repulsions between head groups. The latter are of electrostatic origin for ionic surfactants and steric for non-ionic surfactants. These two forces tend respectively to diminish or increase the interfacial area per molecule at the water/chain interface. The result is an optimal interfacial area Uq. 

To derive the interfacial equation of state of the monolayer, relating n, F (or the interfacial area per molecule), and T, we need to know the functionality T(c). In Chapter 14, equations for T(c) at constant T, so-called adsorption-isotherm equations, are derived and discussed. Thus, anticipating Equation 14.25 for an ideally dilnted monolayer, the following equation of state is derived ... 

We now assume that the area per molecule in the mixed layer at the cmc and in the layers of single surfactants at their cmc is equal, i.e. Ai = A2 = A. Combination of Equations 3 and A with Equations 9 and 10 then gives the following expression for the interfacial tension ... 

Figure 6. (a) Interfacial pressure vs mean area per molecule... 

Figure 8-10 2H NMR spectra of dimyristoyl phosphatidyl-cholme-d27/water in lamellar phases at 40°C. One chain of the phosphatidylcholine is fully deuterated, containing 27 atoms of 2H. The mole ratios of water to lipid were 5.0 in (A) and 25.0 in (B). The average interfacial areas per alkyl chain as measured hy X-ray diffraction were 0.252 nm2 for (A) and 0.313 nm2 for (B). 2H NMR spectra are presented as "powder patterns" because the lipid molecules are randomly oriented in the magnetic field of the spectrometer as if in a powder. This gives rise to pairs of peaks symmetrically located on both sides of the origin. The separation distances are a measure of the quadrupole splitting of the NMR absorption line caused by the 2H nucleus. The various splittings of the resonances of the 13 -CH2- and one -CH3 groups reflect differences in mobility.109 The peaks have been assigned tentatively as indicated. From Boden, Jones, and Sixl.115 Courtesy of N. Boden.

Early work predicted smectic (or lamellar) ordering in rod-coil copolymers (Semenov 1991 Semenov and Vasilenko 1986). In liquid crystals, a smectic A phase is a lamellar phase where the molecules are, on average, parallel to the layer normal. In a smectic C phase, the molecules are tilted with respect to this direction. The imbalance in interfacial area per chain for a rod or coil can lead to tilting of chains to maintain uniform density. Semenov (1991) constructed a phase diagram for rod-coil copolymers in which second-order phase transitions... 

Photochemical processes in monolayers at the air-water interface can be controlled externally by variation of the various parameters like matrix composition, subphase composition, temperature and surface pressure. When the product of the reactions has a different area per molecule, the surface pressure may change at constant monolayer area. An interfacial shock wave has been generated in this way. This technique permits the investigation of the kinetics of reorganization processes and the transmission of mechanical signals in monolayers. 

The decrease in interfacial tension is related to the amount of extractant adsorbed at the interface through the Gibb s adsorption equation (46). The molecular areas of the extractant at the interface can thus be directly obtained from this equation. As an example, an area of 104 8 A2 is obtained for the. V,.V -dimc(hyl dibu-tyltetradecylmalonamide (DMDBTDMA) at the dodecane/water interface (4, 34). For classical surfactants, it should be noted that a nearly constant area per molecule with the addition of salt strongly suggests that anions and cations are adsorbed and extracted as pairs (47). Thus, the variation of the area per molecule with added salt can provide information on the mechanism of extraction. 

The energy plotted in Figure 3.3 was obtained by multiplying the total area by the interfacial tension. Suppose now that a small quantity of a surfactant was added to the water, possibly a few tenths of a percent, that lowered the interfacial tension to 0.35 mN/m. This would lower the amount of mechanical energy needed in the above example by a factor of 100. From the area per molecule that the adsorbed emulsifying agent occupies, the minimum amount of emulsifier needed for the emulsion can also be estimated. 

Here y is a generalized interfacial tension, Ci and C2 are bending stresses associated with the curvatures ci and eg, respectively A is the internal interfacial area per unit volume of microemulsion ui and ni are the chemical potentials per molecule and the number of molecules of species i, respectively 0 is the volume fraction of the dispersed phase and P2 and pi are the pressures inside the globules and in the continuous phase in the space between the globules. Here the actual physical surface of the globule (to the extent to which it can be defined) of radius r is selected as the Gibbs dividing surface. 

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